Random Variation in a Model

Gamma

The density function of the gamma distribution is

\[ f(x) = \frac{\lambda ^{-\alpha }x^{\alpha - 1}e^{-\frac{x}{\lambda }}}{\Gamma (\alpha )} \]

where $x \ge 0$. The function $\Gamma (z)$ is defined in the section Beta.

Parameters:

$\alpha $

is the shape parameter, $\alpha > 0$.

$\lambda $

is the scale parameter, $\lambda > 0$.

Table B.10 shows how the gamma distribution parameter names are specified in Simulation Studio (specifically, in the Numeric Source block) and in JMP.

Table B.10: Gamma Distribution Parameter Names

 

Simulation Studio

JMP

$\lambda $

Scale

$\sigma $

$\alpha $

Shape

$\alpha $


The following examples show (case-sensitive) string values that can be used as Numeric Source block DataStreamDescription factor values or InStreamPolicy port values. In these examples, the distribution and parameter names in the string value are the names that are used in the Theoretical option in the Numeric Source Block Properties dialog box (including any spaces or hyphens). Quotation marks are not required around the string value, and you can specify only the parameters that need to be updated (as demonstrated in the second example).

  • class == Gamma;Shape == 2;Scale == 1

  • Shape == 2